Least Common Multiple (LCM) of 104 and 175
The least common multiple (LCM) of 104 and 175 is 18200.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 104 and 175?
First, calculate the GCD of 104 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 104 ÷ 175 = 0 remainder 104 |
| 2 | 175 ÷ 104 = 1 remainder 71 |
| 3 | 104 ÷ 71 = 1 remainder 33 |
| 4 | 71 ÷ 33 = 2 remainder 5 |
| 5 | 33 ÷ 5 = 6 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 62 and 144 | 4464 |
| 66 and 15 | 330 |
| 196 and 70 | 980 |
| 139 and 39 | 5421 |
| 68 and 185 | 12580 |